LMFDB - Embedded newform 354.2.c.b.353.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,2,Mod(353,354)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("354.353");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	354.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.82670423155$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	10.0.41542366334681088.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} - x^{8} - 2x^{7} + 2x^{6} + 14x^{5} + 6x^{4} - 18x^{3} - 27x^{2} - 81x + 243 $ x^10 - x^9 - x^8 - 2x^7 + 2x^6 + 14x^5 + 6x^4 - 18x^3 - 27x^2 - 81*x + 243
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			353.1
Root			$1.65530 - 0.509894i$ of defining polynomial
Character	$\chi$	$=$	354.353
Dual form			354.2.c.b.353.2

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(-1.65530 - 0.509894i) q^{3} +1.00000 q^{4} +2.90260i q^{5} +(-1.65530 - 0.509894i) q^{6} -3.06916 q^{7} +1.00000 q^{8} +(2.48002 + 1.68805i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(-1.65530 - 0.509894i) q^{3} +1.00000 q^{4} +2.90260i q^{5} +(-1.65530 - 0.509894i) q^{6} -3.06916 q^{7} +1.00000 q^{8} +(2.48002 + 1.68805i) q^{9} +2.90260i q^{10} -1.35591 q^{11} +(-1.65530 - 0.509894i) q^{12} +7.06097i q^{13} -3.06916 q^{14} +(1.48002 - 4.80466i) q^{15} +1.00000 q^{16} +0.568263i q^{17} +(2.48002 + 1.68805i) q^{18} -4.42507 q^{19} +2.90260i q^{20} +(5.08036 + 1.56494i) q^{21} -1.35591 q^{22} +7.20070 q^{23} +(-1.65530 - 0.509894i) q^{24} -3.42507 q^{25} +7.06097i q^{26} +(-3.24444 - 4.05877i) q^{27} -3.06916 q^{28} -2.41581i q^{29} +(1.48002 - 4.80466i) q^{30} +6.44875i q^{31} +1.00000 q^{32} +(2.24444 + 0.691371i) q^{33} +0.568263i q^{34} -8.90852i q^{35} +(2.48002 + 1.68805i) q^{36} +1.74257i q^{37} -4.42507 q^{38} +(3.60035 - 11.6880i) q^{39} +2.90260i q^{40} -8.09404i q^{41} +(5.08036 + 1.56494i) q^{42} +0.770515i q^{43} -1.35591 q^{44} +(-4.89973 + 7.19849i) q^{45} +7.20070 q^{46} +4.48887 q^{47} +(-1.65530 - 0.509894i) q^{48} +2.41972 q^{49} -3.42507 q^{50} +(0.289754 - 0.940644i) q^{51} +7.06097i q^{52} -1.03307i q^{53} +(-3.24444 - 4.05877i) q^{54} -3.93566i q^{55} -3.06916 q^{56} +(7.32480 + 2.25631i) q^{57} -2.41581i q^{58} +(3.07451 + 7.03899i) q^{59} +(1.48002 - 4.80466i) q^{60} -10.6746i q^{61} +6.44875i q^{62} +(-7.61156 - 5.18089i) q^{63} +1.00000 q^{64} -20.4952 q^{65} +(2.24444 + 0.691371i) q^{66} +1.09256i q^{67} +0.568263i q^{68} +(-11.9193 - 3.67159i) q^{69} -8.90852i q^{70} -11.0406i q^{71} +(2.48002 + 1.68805i) q^{72} -5.96044i q^{73} +1.74257i q^{74} +(5.66950 + 1.74642i) q^{75} -4.42507 q^{76} +4.16150 q^{77} +(3.60035 - 11.6880i) q^{78} +8.62041 q^{79} +2.90260i q^{80} +(3.30096 + 8.37279i) q^{81} -8.09404i q^{82} -14.6504 q^{83} +(5.08036 + 1.56494i) q^{84} -1.64944 q^{85} +0.770515i q^{86} +(-1.23181 + 3.99888i) q^{87} -1.35591 q^{88} +11.5174 q^{89} +(-4.89973 + 7.19849i) q^{90} -21.6712i q^{91} +7.20070 q^{92} +(3.28818 - 10.6746i) q^{93} +4.48887 q^{94} -12.8442i q^{95} +(-1.65530 - 0.509894i) q^{96} +8.16151i q^{97} +2.41972 q^{98} +(-3.36268 - 2.28885i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 10 q^{2} - q^{3} + 10 q^{4} - q^{6} - 2 q^{7} + 10 q^{8} + 3 q^{9}+O(q^{10}) $ 10 * q + 10 * q^2 - q^3 + 10 * q^4 - q^6 - 2 * q^7 + 10 * q^8 + 3 * q^9	$ 10 q + 10 q^{2} - q^{3} + 10 q^{4} - q^{6} - 2 q^{7} + 10 q^{8} + 3 q^{9} - 4 q^{11} - q^{12} - 2 q^{14} - 7 q^{15} + 10 q^{16} + 3 q^{18} - 6 q^{19} - 3 q^{21} - 4 q^{22} + 8 q^{23} - q^{24} + 4 q^{25} - 10 q^{27} - 2 q^{28} - 7 q^{30} + 10 q^{32} + 3 q^{36} - 6 q^{38} + 4 q^{39} - 3 q^{42} - 4 q^{44} - 11 q^{45} + 8 q^{46} - q^{48} + 8 q^{49} + 4 q^{50} + 2 q^{51} - 10 q^{54} - 2 q^{56} - 3 q^{57} - 20 q^{59} - 7 q^{60} - 19 q^{63} + 10 q^{64} - 16 q^{65} - 14 q^{69} + 3 q^{72} - 4 q^{75} - 6 q^{76} - 48 q^{77} + 4 q^{78} + 6 q^{79} + 7 q^{81} - 12 q^{83} - 3 q^{84} - 4 q^{85} - 15 q^{87} - 4 q^{88} + 16 q^{89} - 11 q^{90} + 8 q^{92} + 52 q^{93} - q^{96} + 8 q^{98} - 2 q^{99}+O(q^{100}) $ 10 * q + 10 * q^2 - q^3 + 10 * q^4 - q^6 - 2 * q^7 + 10 * q^8 + 3 * q^9 - 4 * q^11 - q^12 - 2 * q^14 - 7 * q^15 + 10 * q^16 + 3 * q^18 - 6 * q^19 - 3 * q^21 - 4 * q^22 + 8 * q^23 - q^24 + 4 * q^25 - 10 * q^27 - 2 * q^28 - 7 * q^30 + 10 * q^32 + 3 * q^36 - 6 * q^38 + 4 * q^39 - 3 * q^42 - 4 * q^44 - 11 * q^45 + 8 * q^46 - q^48 + 8 * q^49 + 4 * q^50 + 2 * q^51 - 10 * q^54 - 2 * q^56 - 3 * q^57 - 20 * q^59 - 7 * q^60 - 19 * q^63 + 10 * q^64 - 16 * q^65 - 14 * q^69 + 3 * q^72 - 4 * q^75 - 6 * q^76 - 48 * q^77 + 4 * q^78 + 6 * q^79 + 7 * q^81 - 12 * q^83 - 3 * q^84 - 4 * q^85 - 15 * q^87 - 4 * q^88 + 16 * q^89 - 11 * q^90 + 8 * q^92 + 52 * q^93 - q^96 + 8 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/354\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	−1.65530	−	0.509894i	−0.955686	−	0.294387i
$3$	−1.65530	−	0.509894i	−0.955686	−	0.294387i
$4$	1.00000			0.500000
$5$			2.90260i			1.29808i	0.760754	+	0.649040i	$0.224829\pi$
$5$			2.90260i			1.29808i	−0.760754	+	0.649040i	$0.775171\pi$
$6$	−1.65530	−	0.509894i	−0.675772	−	0.208163i
$7$	−3.06916			−1.16003			−0.580016	−	0.814605i	$-0.696954\pi$
$7$	−3.06916			−1.16003			−0.580016	+	0.814605i	$0.696954\pi$
$8$	1.00000			0.353553
$9$	2.48002	+	1.68805i	0.826672	+	0.562684i
$10$			2.90260i			0.917882i
$11$	−1.35591			−0.408823			−0.204411	−	0.978885i	$-0.565528\pi$
$11$	−1.35591			−0.408823			−0.204411	+	0.978885i	$0.565528\pi$
$12$	−1.65530	−	0.509894i	−0.477843	−	0.147194i
$13$			7.06097i			1.95836i	0.202989	+	0.979181i	$0.434934\pi$
$13$			7.06097i			1.95836i	−0.202989	+	0.979181i	$0.565066\pi$
$14$	−3.06916			−0.820266
$15$	1.48002	−	4.80466i	0.382139	−	1.24056i
$16$	1.00000			0.250000
$17$			0.568263i			0.137824i	0.997623	+	0.0689120i	$0.0219528\pi$
$17$			0.568263i			0.137824i	−0.997623	+	0.0689120i	$0.978047\pi$
$18$	2.48002	+	1.68805i	0.584545	+	0.397878i
$19$	−4.42507			−1.01518			−0.507590	−	0.861599i	$-0.669464\pi$
$19$	−4.42507			−1.01518			−0.507590	+	0.861599i	$0.669464\pi$
$20$			2.90260i			0.649040i
$21$	5.08036	+	1.56494i	1.10863	+	0.341499i
$22$	−1.35591			−0.289081
$23$	7.20070			1.50145			0.750724	−	0.660615i	$-0.229705\pi$
$23$	7.20070			1.50145			0.750724	+	0.660615i	$0.229705\pi$
$24$	−1.65530	−	0.509894i	−0.337886	−	0.104082i
$25$	−3.42507			−0.685013
$26$			7.06097i			1.38477i
$27$	−3.24444	−	4.05877i	−0.624392	−	0.781111i
$28$	−3.06916			−0.580016
$29$		−	2.41581i		−	0.448605i	−0.974520	−	0.224302i	$-0.927990\pi$
$29$		−	2.41581i		−	0.448605i	0.974520	−	0.224302i	$-0.0720103\pi$
$30$	1.48002	−	4.80466i	0.270213	−	0.877207i
$31$			6.44875i			1.15823i	0.815246	+	0.579115i	$0.196602\pi$
$31$			6.44875i			1.15823i	−0.815246	+	0.579115i	$0.803398\pi$
$32$	1.00000			0.176777
$33$	2.24444	+	0.691371i	0.390706	+	0.120352i
$34$			0.568263i			0.0974563i
$35$		−	8.90852i		−	1.50581i
$36$	2.48002	+	1.68805i	0.413336	+	0.281342i
$37$			1.74257i			0.286476i	0.989688	+	0.143238i	$0.0457515\pi$
$37$			1.74257i			0.286476i	−0.989688	+	0.143238i	$0.954248\pi$
$38$	−4.42507			−0.717841
$39$	3.60035	−	11.6880i	0.576517	−	1.87158i
$40$			2.90260i			0.458941i
$41$		−	8.09404i		−	1.26408i	−0.774937	−	0.632039i	$-0.782218\pi$
$41$		−	8.09404i		−	1.26408i	0.774937	−	0.632039i	$-0.217782\pi$
$42$	5.08036	+	1.56494i	0.783917	+	0.241476i
$43$			0.770515i			0.117502i	0.998273	+	0.0587512i	$0.0187119\pi$
$43$			0.770515i			0.117502i	−0.998273	+	0.0587512i	$0.981288\pi$
$44$	−1.35591			−0.204411
$45$	−4.89973	+	7.19849i	−0.730409	+	1.07309i
$46$	7.20070			1.06168
$47$	4.48887			0.654769			0.327385	−	0.944891i	$-0.393833\pi$
$47$	4.48887			0.654769			0.327385	+	0.944891i	$0.393833\pi$
$48$	−1.65530	−	0.509894i	−0.238922	−	0.0735968i
$49$	2.41972			0.345674
$50$	−3.42507			−0.484378
$51$	0.289754	−	0.940644i	0.0405737	−	0.131717i
$52$			7.06097i			0.979181i
$53$		−	1.03307i		−	0.141903i	−0.997480	−	0.0709514i	$-0.977396\pi$
$53$		−	1.03307i		−	0.141903i	0.997480	−	0.0709514i	$-0.0226035\pi$
$54$	−3.24444	−	4.05877i	−0.441512	−	0.552329i
$55$		−	3.93566i		−	0.530685i
$56$	−3.06916			−0.410133
$57$	7.32480	+	2.25631i	0.970194	+	0.298856i
$58$		−	2.41581i		−	0.317211i
$59$	3.07451	+	7.03899i	0.400267	+	0.916399i
$59$	3.07451	+	7.03899i	0.400267	+	0.916399i
$60$	1.48002	−	4.80466i	0.191069	−	0.620279i
$61$		−	10.6746i		−	1.36674i	−0.730072	−	0.683371i	$-0.760513\pi$
$61$		−	10.6746i		−	1.36674i	0.730072	−	0.683371i	$-0.239487\pi$
$62$			6.44875i			0.818992i
$63$	−7.61156	−	5.18089i	−0.958966	−	0.652731i
$64$	1.00000			0.125000
$65$	−20.4952			−2.54211
$66$	2.24444	+	0.691371i	0.276271	+	0.0851019i
$67$			1.09256i			0.133478i	0.997770	+	0.0667388i	$0.0212594\pi$
$67$			1.09256i			0.133478i	−0.997770	+	0.0667388i	$0.978741\pi$
$68$			0.568263i			0.0689120i
$69$	−11.9193	−	3.67159i	−1.43491	−	0.442008i
$70$		−	8.90852i		−	1.06477i
$71$		−	11.0406i		−	1.31028i	−0.755508	−	0.655139i	$-0.772610\pi$
$71$		−	11.0406i		−	1.31028i	0.755508	−	0.655139i	$-0.227390\pi$
$72$	2.48002	+	1.68805i	0.292273	+	0.198939i
$73$		−	5.96044i		−	0.697617i	−0.937194	−	0.348808i	$-0.886586\pi$
$73$		−	5.96044i		−	0.697617i	0.937194	−	0.348808i	$-0.113414\pi$
$74$			1.74257i			0.202569i
$75$	5.66950	+	1.74642i	0.654658	+	0.201659i
$76$	−4.42507			−0.507590
$77$	4.16150			0.474247
$78$	3.60035	−	11.6880i	0.407659	−	1.32341i
$79$	8.62041			0.969872			0.484936	−	0.874550i	$-0.338843\pi$
$79$	8.62041			0.969872			0.484936	+	0.874550i	$0.338843\pi$
$80$			2.90260i			0.324520i
$81$	3.30096	+	8.37279i	0.366774	+	0.930310i
$82$		−	8.09404i		−	0.893837i
$83$	−14.6504			−1.60809			−0.804044	−	0.594570i	$-0.797322\pi$
$83$	−14.6504			−1.60809			−0.804044	+	0.594570i	$0.797322\pi$
$84$	5.08036	+	1.56494i	0.554313	+	0.170749i
$85$	−1.64944			−0.178907
$86$			0.770515i			0.0830867i
$87$	−1.23181	+	3.99888i	−0.132064	+	0.428725i
$88$	−1.35591			−0.144541
$89$	11.5174			1.22084			0.610422	−	0.792077i	$-0.291000\pi$
$89$	11.5174			1.22084			0.610422	+	0.792077i	$0.291000\pi$
$90$	−4.89973	+	7.19849i	−0.516477	+	0.758787i
$91$		−	21.6712i		−	2.27176i
$92$	7.20070			0.750724
$93$	3.28818	−	10.6746i	0.340968	−	1.10690i
$94$	4.48887			0.462992
$95$		−	12.8442i		−	1.31779i
$96$	−1.65530	−	0.509894i	−0.168943	−	0.0520408i
$97$			8.16151i			0.828676i	0.910123	+	0.414338i	$0.135987\pi$
$97$			8.16151i			0.828676i	−0.910123	+	0.414338i	$0.864013\pi$
$98$	2.41972			0.244428
$99$	−3.36268	−	2.28885i	−0.337962	−	0.230038i
$100$	−3.42507			−0.342507
$101$	10.1615			1.01111			0.505554	−	0.862795i	$-0.331288\pi$
$101$	10.1615			1.01111			0.505554	+	0.862795i	$0.331288\pi$
$102$	0.289754	−	0.940644i	0.0286899	−	0.0931377i
$103$			16.6350i			1.63910i	0.573009	+	0.819549i	$0.305776\pi$
$103$			16.6350i			1.63910i	−0.573009	+	0.819549i	$0.694224\pi$
$104$			7.06097i			0.692386i
$105$	−4.54240	+	14.7462i	−0.443293	+	1.43909i
$106$		−	1.03307i		−	0.100340i
$107$			19.5376i			1.88877i	0.328836	+	0.944387i	$0.393344\pi$
$107$			19.5376i			1.88877i	−0.328836	+	0.944387i	$0.606656\pi$
$108$	−3.24444	−	4.05877i	−0.312196	−	0.390556i
$109$			1.42258i			0.136259i	0.997676	+	0.0681293i	$0.0217030\pi$
$109$			1.42258i			0.136259i	−0.997676	+	0.0681293i	$0.978297\pi$
$110$		−	3.93566i		−	0.375251i
$111$	0.888525	−	2.88447i	0.0843350	−	0.273782i
$112$	−3.06916			−0.290008
$113$	16.6379			1.56516			0.782580	−	0.622550i	$-0.213903\pi$
$113$	16.6379			1.56516			0.782580	+	0.622550i	$0.213903\pi$
$114$	7.32480	+	2.25631i	0.686030	+	0.211323i
$115$			20.9007i			1.94900i
$116$		−	2.41581i		−	0.224302i
$117$	−11.9193	+	17.5113i	−1.10194	+	1.61892i
$118$	3.07451	+	7.03899i	0.283031	+	0.647992i
$119$		−	1.74409i		−	0.159880i
$120$	1.48002	−	4.80466i	0.135106	−	0.438603i
$121$	−9.16150			−0.832864
$122$		−	10.6746i		−	0.966432i
$123$	−4.12710	+	13.3980i	−0.372128	+	1.20806i
$124$			6.44875i			0.579115i
$125$			4.57139i			0.408878i
$126$	−7.61156	−	5.18089i	−0.678091	−	0.461551i
$127$	8.29304			0.735889			0.367944	−	0.929848i	$-0.380062\pi$
$127$	8.29304			0.735889			0.367944	+	0.929848i	$0.380062\pi$
$128$	1.00000			0.0883883
$129$	0.392881	−	1.27543i	0.0345912	−	0.112295i
$130$	−20.4952			−1.79754
$131$	10.0063			0.874253			0.437127	−	0.899400i	$-0.355996\pi$
$131$	10.0063			0.874253			0.437127	+	0.899400i	$0.355996\pi$
$132$	2.24444	+	0.691371i	0.195353	+	0.0601761i
$133$	13.5812			1.17764
$134$			1.09256i			0.0943830i
$135$	11.7810	−	9.41729i	1.01395	−	0.810511i
$136$			0.568263i			0.0487282i
$137$			12.8067i			1.09415i	0.837084	+	0.547074i	$0.184258\pi$
$137$			12.8067i			1.09415i	−0.837084	+	0.547074i	$0.815742\pi$
$138$	−11.9193	−	3.67159i	−1.01464	−	0.312547i
$139$	8.09377			0.686505			0.343252	−	0.939243i	$-0.388471\pi$
$139$	8.09377			0.686505			0.343252	+	0.939243i	$0.388471\pi$
$140$		−	8.90852i		−	0.752907i
$141$	−7.43042	−	2.28885i	−0.625754	−	0.192756i
$142$		−	11.0406i		−	0.926507i
$143$		−	9.57406i		−	0.800623i
$144$	2.48002	+	1.68805i	0.206668	+	0.140671i
$145$	7.01212			0.582325
$146$		−	5.96044i		−	0.493290i
$147$	−4.00535	−	1.23380i	−0.330356	−	0.101762i
$148$			1.74257i			0.143238i
$149$	−12.4139			−1.01698			−0.508492	−	0.861066i	$-0.669797\pi$
$149$	−12.4139			−1.01698			−0.508492	+	0.861066i	$0.669797\pi$
$150$	5.66950	+	1.74642i	0.462913	+	0.142595i
$151$		−	6.74099i		−	0.548574i	−0.961648	−	0.274287i	$-0.911558\pi$
$151$		−	6.74099i		−	0.548574i	0.961648	−	0.274287i	$-0.0884418\pi$
$152$	−4.42507			−0.358920
$153$	−0.959258	+	1.40930i	−0.0775514	+	0.113935i
$154$	4.16150			0.335344
$155$	−18.7181			−1.50347
$156$	3.60035	−	11.6880i	0.288259	−	0.935790i
$157$			4.18807i			0.334244i	0.985936	+	0.167122i	$0.0534474\pi$
$157$			4.18807i			0.334244i	−0.985936	+	0.167122i	$0.946553\pi$
$158$	8.62041			0.685803
$159$	−0.526755	+	1.71003i	−0.0417744	+	0.135615i
$160$			2.90260i			0.229470i
$161$	−22.1001			−1.74173
$162$	3.30096	+	8.37279i	0.259348	+	0.657829i
$163$	−1.85728			−0.145473			−0.0727365	−	0.997351i	$-0.523173\pi$
$163$	−1.85728			−0.145473			−0.0727365	+	0.997351i	$0.523173\pi$
$164$		−	8.09404i		−	0.632039i
$165$	−2.00677	+	6.51469i	−0.156227	+	0.507168i
$166$	−14.6504			−1.13709
$167$		−	7.28369i		−	0.563629i	−0.959469	−	0.281814i	$-0.909064\pi$
$167$		−	7.28369i		−	0.563629i	0.959469	−	0.281814i	$-0.0909362\pi$
$168$	5.08036	+	1.56494i	0.391959	+	0.120738i
$169$	−36.8574			−2.83518
$170$	−1.64944			−0.126506
$171$	−10.9742	−	7.46974i	−0.839221	−	0.571225i
$172$			0.770515i			0.0587512i
$173$	21.8511			1.66131			0.830653	−	0.556790i	$-0.187967\pi$
$173$	21.8511			1.66131			0.830653	+	0.556790i	$0.187967\pi$
$174$	−1.23181	+	3.99888i	−0.0933830	+	0.303155i
$175$	10.5121			0.794637
$176$	−1.35591			−0.102206
$177$	−1.50008	−	13.2193i	−0.112753	−	0.993623i
$178$	11.5174			0.863267
$179$	17.9386			1.34079			0.670395	−	0.742004i	$-0.266125\pi$
$179$	17.9386			1.34079			0.670395	+	0.742004i	$0.266125\pi$
$180$	−4.89973	+	7.19849i	−0.365205	+	0.536544i
$181$	1.63018			0.121170			0.0605850	−	0.998163i	$-0.480703\pi$
$181$	1.63018			0.121170			0.0605850	+	0.998163i	$0.480703\pi$
$182$		−	21.6712i		−	1.60638i
$183$	−5.44291	+	17.6696i	−0.402351	+	1.30618i
$184$	7.20070			0.530842
$185$	−5.05797			−0.371869
$186$	3.28818	−	10.6746i	0.241101	−	0.782699i
$187$		−	0.770515i		−	0.0563456i
$188$	4.48887			0.327385
$189$	9.95768	+	12.4570i	0.724315	+	0.906114i
$190$		−	12.8442i		−	0.931815i
$191$	−4.94832			−0.358048			−0.179024	−	0.983845i	$-0.557294\pi$
$191$	−4.94832			−0.358048			−0.179024	+	0.983845i	$0.557294\pi$
$192$	−1.65530	−	0.509894i	−0.119461	−	0.0367984i
$193$	−7.55803			−0.544039			−0.272019	−	0.962292i	$-0.587691\pi$
$193$	−7.55803			−0.544039			−0.272019	+	0.962292i	$0.587691\pi$
$194$			8.16151i			0.585962i
$195$	33.9256	+	10.4504i	2.42946	+	0.748366i
$196$	2.41972			0.172837
$197$			6.53668i			0.465719i	0.972510	+	0.232859i	$0.0748082\pi$
$197$			6.53668i			0.465719i	−0.972510	+	0.232859i	$0.925192\pi$
$198$	−3.36268	−	2.28885i	−0.238975	−	0.162661i
$199$	−16.9942			−1.20468			−0.602342	−	0.798238i	$-0.705766\pi$
$199$	−16.9942			−1.20468			−0.602342	+	0.798238i	$0.705766\pi$
$200$	−3.42507			−0.242189
$201$	0.557091	−	1.80851i	0.0392941	−	0.127563i
$202$	10.1615			0.714961
$203$			7.41450i			0.520396i
$204$	0.289754	−	0.940644i	0.0202868	−	0.0658583i
$205$	23.4937			1.64087
$206$			16.6350i			1.15902i
$207$	17.8578	+	12.1551i	1.24121	+	0.844841i
$208$			7.06097i			0.489590i
$209$	6.00000			0.415029
$210$	−4.54240	+	14.7462i	−0.313455	+	1.01759i
$211$		−	27.9219i		−	1.92222i	−0.276167	−	0.961110i	$-0.589064\pi$
$211$		−	27.9219i		−	1.92222i	0.276167	−	0.961110i	$-0.410936\pi$
$212$		−	1.03307i		−	0.0709514i
$213$	−5.62954	+	18.2755i	−0.385729	+	1.25222i
$214$			19.5376i			1.33556i
$215$	−2.23649			−0.152528
$216$	−3.24444	−	4.05877i	−0.220756	−	0.276164i
$217$		−	19.7922i		−	1.34358i
$218$			1.42258i			0.0963494i
$219$	−3.03919	+	9.86630i	−0.205370	+	0.666703i
$220$		−	3.93566i		−	0.265342i
$221$	−4.01249			−0.269909
$222$	0.888525	−	2.88447i	0.0596339	−	0.193593i
$223$	−21.6281			−1.44833			−0.724163	−	0.689629i	$-0.757774\pi$
$223$	−21.6281			−1.44833			−0.724163	+	0.689629i	$0.757774\pi$
$224$	−3.06916			−0.205067
$225$	−8.49422	−	5.78169i	−0.566282	−	0.385446i
$226$	16.6379			1.10674
$227$	−0.476381			−0.0316185			−0.0158093	−	0.999875i	$-0.505032\pi$
$227$	−0.476381			−0.0316185			−0.0158093	+	0.999875i	$0.505032\pi$
$228$	7.32480	+	2.25631i	0.485097	+	0.149428i
$229$			18.0656i			1.19381i	0.802313	+	0.596904i	$0.203603\pi$
$229$			18.0656i			1.19381i	−0.802313	+	0.596904i	$0.796397\pi$
$230$			20.9007i			1.37815i
$231$	−6.88852	−	2.12193i	−0.453232	−	0.139612i
$232$		−	2.41581i		−	0.158606i
$233$	−7.83229			−0.513111			−0.256555	−	0.966530i	$-0.582588\pi$
$233$	−7.83229			−0.513111			−0.256555	+	0.966530i	$0.582588\pi$
$234$	−11.9193	+	17.5113i	−0.779188	+	1.14475i
$235$			13.0294i			0.849943i
$236$	3.07451	+	7.03899i	0.200133	+	0.458199i
$237$	−14.2693	−	4.39550i	−0.926893	−	0.285518i
$238$		−	1.74409i		−	0.113052i
$239$		−	13.1302i		−	0.849325i	−0.905352	−	0.424662i	$-0.860393\pi$
$239$		−	13.1302i		−	0.849325i	0.905352	−	0.424662i	$-0.139607\pi$
$240$	1.48002	−	4.80466i	0.0955346	−	0.310139i
$241$	12.0024			0.773140			0.386570	−	0.922260i	$-0.373660\pi$
$241$	12.0024			0.773140			0.386570	+	0.922260i	$0.373660\pi$
$242$	−9.16150			−0.588924
$243$	−1.19484	−	15.5426i	−0.0766489	−	0.997058i
$244$		−	10.6746i		−	0.683371i
$245$			7.02346i			0.448713i
$246$	−4.12710	+	13.3980i	−0.263134	+	0.854228i
$247$		−	31.2453i		−	1.98809i
$248$			6.44875i			0.409496i
$249$	24.2507	+	7.47014i	1.53683	+	0.473401i
$250$			4.57139i			0.289120i
$251$			2.86482i			0.180826i	0.995904	+	0.0904129i	$0.0288187\pi$
$251$			2.86482i			0.180826i	−0.995904	+	0.0904129i	$0.971181\pi$
$252$	−7.61156	−	5.18089i	−0.479483	−	0.326366i
$253$	−9.76351			−0.613826
$254$	8.29304			0.520352
$255$	2.73031	+	0.841039i	0.170979	+	0.0526679i
$256$	1.00000			0.0625000
$257$		−	11.8361i		−	0.738318i	−0.929366	−	0.369159i	$-0.879646\pi$
$257$		−	11.8361i		−	0.738318i	0.929366	−	0.369159i	$-0.120354\pi$
$258$	0.392881	−	1.27543i	0.0244597	−	0.0794048i
$259$		−	5.34821i		−	0.332322i
$260$	−20.4952			−1.27106
$261$	4.07801	−	5.99125i	0.252423	−	0.370849i
$262$	10.0063			0.618191
$263$			15.9639i			0.984373i	0.870490	+	0.492187i	$0.163802\pi$
$263$			15.9639i			0.984373i	−0.870490	+	0.492187i	$0.836198\pi$
$264$	2.24444	+	0.691371i	0.138136	+	0.0425509i
$265$	2.99858			0.184201
$266$	13.5812			0.832718
$267$	−19.0647	−	5.87266i	−1.16674	−	0.359401i
$268$			1.09256i			0.0667388i
$269$	−19.1392			−1.16694			−0.583470	−	0.812134i	$-0.698306\pi$
$269$	−19.1392			−1.16694			−0.583470	+	0.812134i	$0.698306\pi$
$270$	11.7810	−	9.41729i	0.716968	−	0.573118i
$271$	16.9434			1.02924			0.514620	−	0.857419i	$-0.327933\pi$
$271$	16.9434			1.02924			0.514620	+	0.857419i	$0.327933\pi$
$272$			0.568263i			0.0344560i
$273$	−11.0500	+	35.8723i	−0.668778	+	2.17109i
$274$			12.8067i			0.773679i
$275$	4.64409			0.280049
$276$	−11.9193	−	3.67159i	−0.717457	−	0.221004i
$277$	17.8471			1.07233			0.536165	−	0.844113i	$-0.319872\pi$
$277$	17.8471			1.07233			0.536165	+	0.844113i	$0.319872\pi$
$278$	8.09377			0.485432
$279$	−10.8858	+	15.9930i	−0.651717	+	0.957476i
$280$		−	8.90852i		−	0.532386i
$281$		−	29.1267i		−	1.73755i	−0.495207	−	0.868775i	$-0.664908\pi$
$281$		−	29.1267i		−	1.73755i	0.495207	−	0.868775i	$-0.335092\pi$
$282$	−7.43042	−	2.28885i	−0.442475	−	0.136299i
$283$			6.45672i			0.383812i	0.981413	+	0.191906i	$0.0614669\pi$
$283$			6.45672i			0.383812i	−0.981413	+	0.191906i	$0.938533\pi$
$284$		−	11.0406i		−	0.655139i
$285$	−6.54917	+	21.2609i	−0.387939	+	1.25939i
$286$		−	9.57406i		−	0.566126i
$287$			24.8419i			1.46637i
$288$	2.48002	+	1.68805i	0.146136	+	0.0994694i
$289$	16.6771			0.981005
$290$	7.01212			0.411766
$291$	4.16150	−	13.5097i	0.243952	−	0.791954i
$292$		−	5.96044i		−	0.348808i
$293$		−	28.9847i		−	1.69331i	−0.532146	−	0.846653i	$-0.678614\pi$
$293$		−	28.9847i		−	1.69331i	0.532146	−	0.846653i	$-0.321386\pi$
$294$	−4.00535	−	1.23380i	−0.233597	−	0.0719566i
$295$	−20.4314	+	8.92405i	−1.18956	+	0.519578i
$296$			1.74257i			0.101285i
$297$	4.39917	+	5.50334i	0.255266	+	0.319336i
$298$	−12.4139			−0.719117
$299$			50.8439i			2.94038i
$300$	5.66950	+	1.74642i	0.327329	+	0.100830i
$301$		−	2.36483i		−	0.136306i
$302$		−	6.74099i		−	0.387900i
$303$	−16.8203	−	5.18129i	−0.966301	−	0.297657i
$304$	−4.42507			−0.253795
$305$	30.9840			1.77414
$306$	−0.959258	+	1.40930i	−0.0548371	+	0.0805644i
$307$	5.63646			0.321690			0.160845	−	0.986980i	$-0.448578\pi$
$307$	5.63646			0.321690			0.160845	+	0.986980i	$0.448578\pi$
$308$	4.16150			0.237124
$309$	8.48210	−	27.5359i	0.482530	−	1.56646i
$310$	−18.7181			−1.06312
$311$		−	11.9919i		−	0.680000i	−0.940425	−	0.340000i	$-0.889573\pi$
$311$		−	11.9919i		−	0.680000i	0.940425	−	0.340000i	$-0.110427\pi$
$312$	3.60035	−	11.6880i	0.203830	−	0.661703i
$313$		−	8.31980i		−	0.470263i	−0.971964	−	0.235131i	$-0.924448\pi$
$313$		−	8.31980i		−	0.470263i	0.971964	−	0.235131i	$-0.0755520\pi$
$314$			4.18807i			0.236346i
$315$	15.0380	−	22.0933i	0.847298	−	1.24482i
$316$	8.62041			0.484936
$317$			26.2936i			1.47680i	0.674365	+	0.738398i	$0.264417\pi$
$317$			26.2936i			1.47680i	−0.674365	+	0.738398i	$0.735583\pi$
$318$	−0.526755	+	1.71003i	−0.0295390	+	0.0958939i
$319$			3.27562i			0.183400i
$320$			2.90260i			0.162260i
$321$	9.96212	−	32.3406i	0.556031	−	1.80508i
$322$	−22.1001			−1.23159
$323$		−	2.51460i		−	0.139916i
$324$	3.30096	+	8.37279i	0.183387	+	0.465155i
$325$		−	24.1843i		−	1.34150i
$326$	−1.85728			−0.102865
$327$	0.725366	−	2.35480i	0.0401128	−	0.130220i
$328$		−	8.09404i		−	0.446919i
$329$	−13.7770			−0.759553
$330$	−2.00677	+	6.51469i	−0.110469	+	0.358622i
$331$	−20.2592			−1.11355			−0.556773	−	0.830665i	$-0.687961\pi$
$331$	−20.2592			−1.11355			−0.556773	+	0.830665i	$0.687961\pi$
$332$	−14.6504			−0.804044
$333$	−2.94154	+	4.32160i	−0.161196	+	0.236822i
$334$		−	7.28369i		−	0.398546i
$335$	−3.17127			−0.173265
$336$	5.08036	+	1.56494i	0.277157	+	0.0853747i
$337$		−	33.0786i		−	1.80190i	−0.433919	−	0.900952i	$-0.642870\pi$
$337$		−	33.0786i		−	1.80190i	0.433919	−	0.900952i	$-0.357130\pi$
$338$	−36.8574			−2.00478
$339$	−27.5406	−	8.48356i	−1.49580	−	0.460764i
$340$	−1.64944			−0.0894534
$341$		−	8.74393i		−	0.473510i
$342$	−10.9742	−	7.46974i	−0.593419	−	0.403917i
$343$	14.0576			0.759039
$344$			0.770515i			0.0415434i
$345$	10.6571	−	34.5969i	0.573762	−	1.86263i
$346$	21.8511			1.17472
$347$	−20.5577			−1.10359			−0.551796	−	0.833979i	$-0.686057\pi$
$347$	−20.5577			−1.10359			−0.551796	+	0.833979i	$0.686057\pi$
$348$	−1.23181	+	3.99888i	−0.0660318	+	0.214363i
$349$			26.3694i			1.41152i	0.708449	+	0.705762i	$0.249395\pi$
$349$			26.3694i			1.41152i	−0.708449	+	0.705762i	$0.750605\pi$
$350$	10.5121			0.561894
$351$	28.6589	−	22.9089i	1.52970	−	1.22279i
$352$	−1.35591			−0.0722703
$353$	16.1784			0.861092			0.430546	−	0.902569i	$-0.358321\pi$
$353$	16.1784			0.861092			0.430546	+	0.902569i	$0.358321\pi$
$354$	−1.50008	−	13.2193i	−0.0797284	−	0.702598i
$355$	32.0464			1.70085
$356$	11.5174			0.610422
$357$	−0.889300	+	2.88698i	−0.0470667	+	0.152795i
$358$	17.9386			0.948082
$359$		−	19.3351i		−	1.02047i	−0.860036	−	0.510234i	$-0.829559\pi$
$359$		−	19.3351i		−	1.02047i	0.860036	−	0.510234i	$-0.170441\pi$
$360$	−4.89973	+	7.19849i	−0.258239	+	0.379394i
$361$	0.581221			0.0305906
$362$	1.63018			0.0856801
$363$	15.1650	+	4.67140i	0.795957	+	0.245185i
$364$		−	21.6712i		−	1.13588i
$365$	17.3008			0.905563
$366$	−5.44291	+	17.6696i	−0.284505	+	0.923606i
$367$		−	7.18946i		−	0.375287i	−0.982237	−	0.187643i	$-0.939915\pi$
$367$		−	7.18946i		−	0.375287i	0.982237	−	0.187643i	$-0.0600849\pi$
$368$	7.20070			0.375362
$369$	13.6632	−	20.0734i	0.711276	−	1.04498i
$370$	−5.05797			−0.262951
$371$			3.17065i			0.164612i
$372$	3.28818	−	10.6746i	0.170484	−	0.553452i
$373$	20.0865			1.04004			0.520020	−	0.854154i	$-0.325924\pi$
$373$	20.0865			1.04004			0.520020	+	0.854154i	$0.325924\pi$
$374$		−	0.770515i		−	0.0398424i
$375$	2.33093	−	7.56702i	0.120369	−	0.390759i
$376$	4.48887			0.231496
$377$	17.0580			0.878530
$378$	9.95768	+	12.4570i	0.512168	+	0.640719i
$379$	2.68186			0.137758			0.0688789	−	0.997625i	$-0.478058\pi$
$379$	2.68186			0.137758			0.0688789	+	0.997625i	$0.478058\pi$
$380$		−	12.8442i		−	0.658893i
$381$	−13.7275	−	4.22857i	−0.703279	−	0.216636i
$382$	−4.94832			−0.253178
$383$		−	22.1048i		−	1.12950i	−0.825261	−	0.564752i	$-0.808972\pi$
$383$		−	22.1048i		−	1.12950i	0.825261	−	0.564752i	$-0.191028\pi$
$384$	−1.65530	−	0.509894i	−0.0844715	−	0.0260204i
$385$			12.0792i			0.615611i
$386$	−7.55803			−0.384694
$387$	−1.30067	+	1.91089i	−0.0661167	+	0.0971359i
$388$			8.16151i			0.414338i
$389$		−	1.33259i		−	0.0675651i	−0.999429	−	0.0337825i	$-0.989245\pi$
$389$		−	1.33259i		−	0.0675651i	0.999429	−	0.0337825i	$-0.0107554\pi$
$390$	33.9256	+	10.4504i	1.71789	+	0.529174i
$391$			4.09189i			0.206936i
$392$	2.41972			0.122214
$393$	−16.5634	−	5.10215i	−0.835512	−	0.257369i
$394$			6.53668i			0.329313i
$395$			25.0216i			1.25897i
$396$	−3.36268	−	2.28885i	−0.168981	−	0.115019i
$397$		−	25.3810i		−	1.27384i	−0.770931	−	0.636919i	$-0.780209\pi$
$397$		−	25.3810i		−	1.27384i	0.770931	−	0.636919i	$-0.219791\pi$
$398$	−16.9942			−0.851841
$399$	−22.4810	−	6.92498i	−1.12546	−	0.346683i
$400$	−3.42507			−0.171253
$401$	−14.2292			−0.710574			−0.355287	−	0.934757i	$-0.615617\pi$
$401$	−14.2292			−0.710574			−0.355287	+	0.934757i	$0.615617\pi$
$402$	0.557091	−	1.80851i	0.0277852	−	0.0902005i
$403$	−45.5344			−2.26823
$404$	10.1615			0.505554
$405$	−24.3028	+	9.58136i	−1.20762	+	0.476102i
$406$			7.41450i			0.367975i
$407$		−	2.36277i		−	0.117118i
$408$	0.289754	−	0.940644i	0.0143450	−	0.0465688i
$409$			15.8746i			0.784946i	0.919764	+	0.392473i	$0.128380\pi$
$409$			15.8746i			0.784946i	−0.919764	+	0.392473i	$0.871620\pi$
$410$	23.4937			1.16027
$411$	6.53004	−	21.1988i	0.322103	−	1.04566i
$412$			16.6350i			0.819549i
$413$	−9.43614	−	21.6038i	−0.464322	−	1.06305i
$414$	17.8578	+	12.1551i	0.877665	+	0.597393i
$415$		−	42.5241i		−	2.08743i
$416$			7.06097i			0.346193i
$417$	−13.3976	−	4.12696i	−0.656083	−	0.202098i
$418$	6.00000			0.293470
$419$	−16.8244			−0.821924			−0.410962	−	0.911652i	$-0.634807\pi$
$419$	−16.8244			−0.821924			−0.410962	+	0.911652i	$0.634807\pi$
$420$	−4.54240	+	14.7462i	−0.221646	+	0.719543i
$421$			4.37616i			0.213281i	0.994298	+	0.106640i	$0.0340094\pi$
$421$			4.37616i			0.213281i	−0.994298	+	0.106640i	$0.965991\pi$
$422$		−	27.9219i		−	1.35921i
$423$	11.1325	+	7.57745i	0.541280	+	0.368428i
$424$		−	1.03307i		−	0.0501702i
$425$		−	1.94634i		−	0.0944113i
$426$	−5.62954	+	18.2755i	−0.272752	+	0.885450i
$427$			32.7620i			1.58546i
$428$			19.5376i			0.944387i
$429$	−4.88175	+	15.8479i	−0.235693	+	0.765144i
$430$	−2.23649			−0.107853
$431$	−2.04895			−0.0986947			−0.0493473	−	0.998782i	$-0.515714\pi$
$431$	−2.04895			−0.0986947			−0.0493473	+	0.998782i	$0.515714\pi$
$432$	−3.24444	−	4.05877i	−0.156098	−	0.195278i
$433$	−29.6427			−1.42454			−0.712269	−	0.701907i	$-0.752332\pi$
$433$	−29.6427			−1.42454			−0.712269	+	0.701907i	$0.752332\pi$
$434$		−	19.7922i		−	0.950056i
$435$	−11.6071	−	3.57544i	−0.556520	−	0.171429i
$436$			1.42258i			0.0681293i
$437$	−31.8636			−1.52424
$438$	−3.03919	+	9.86630i	−0.145218	+	0.471430i
$439$	−22.0490			−1.05234			−0.526172	−	0.850378i	$-0.676373\pi$
$439$	−22.0490			−1.05234			−0.526172	+	0.850378i	$0.676373\pi$
$440$		−	3.93566i		−	0.187625i
$441$	6.00094	+	4.08461i	0.285759	+	0.194505i
$442$	−4.01249			−0.190855
$443$	8.23544			0.391278			0.195639	−	0.980676i	$-0.437322\pi$
$443$	8.23544			0.391278			0.195639	+	0.980676i	$0.437322\pi$
$444$	0.888525	−	2.88447i	0.0421675	−	0.136891i
$445$			33.4304i			1.58475i
$446$	−21.6281			−1.02412
$447$	20.5487	+	6.32976i	0.971918	+	0.299388i
$448$	−3.06916			−0.145004
$449$		−	1.44717i		−	0.0682961i	−0.999417	−	0.0341481i	$-0.989128\pi$
$449$		−	1.44717i		−	0.0682961i	0.999417	−	0.0341481i	$-0.0108718\pi$
$450$	−8.49422	−	5.78169i	−0.400422	−	0.272552i
$451$			10.9748i			0.516783i
$452$	16.6379			0.782580
$453$	−3.43719	+	11.1583i	−0.161493	+	0.524264i
$454$	−0.476381			−0.0223577
$455$	62.9028			2.94893
$456$	7.32480	+	2.25631i	0.343015	+	0.105662i
$457$			22.1516i			1.03621i	0.855318	+	0.518103i	$0.173362\pi$
$457$			22.1516i			1.03621i	−0.855318	+	0.518103i	$0.826638\pi$
$458$			18.0656i			0.844149i
$459$	2.30645	−	1.84369i	0.107656	−	0.0860563i
$460$			20.9007i			0.974501i
$461$		−	17.2878i		−	0.805174i	−0.915382	−	0.402587i	$-0.868111\pi$
$461$		−	17.2878i		−	0.805174i	0.915382	−	0.402587i	$-0.131889\pi$
$462$	−6.88852	−	2.12193i	−0.320483	−	0.0987209i
$463$			14.3744i			0.668033i	0.942567	+	0.334016i	$0.108404\pi$
$463$			14.3744i			0.668033i	−0.942567	+	0.334016i	$0.891596\pi$
$464$		−	2.41581i		−	0.112151i
$465$	30.9840	+	9.54425i	1.43685	+	0.442604i
$466$	−7.83229			−0.362824
$467$	−23.6209			−1.09304			−0.546522	−	0.837445i	$-0.684048\pi$
$467$	−23.6209			−1.09304			−0.546522	+	0.837445i	$0.684048\pi$
$468$	−11.9193	+	17.5113i	−0.550969	+	0.809462i
$469$		−	3.35324i		−	0.154838i
$470$			13.0294i			0.601001i
$471$	2.13547	−	6.93249i	0.0983972	−	0.319432i
$472$	3.07451	+	7.03899i	0.141516	+	0.323996i
$473$		−	1.04475i		−	0.0480376i
$474$	−14.2693	−	4.39550i	−0.655413	−	0.201892i
$475$	15.1562			0.695412
$476$		−	1.74409i		−	0.0799401i
$477$	1.74387	−	2.56202i	0.0798464	−	0.117307i
$478$		−	13.1302i		−	0.600563i
$479$			10.4744i			0.478588i	0.970947	+	0.239294i	$0.0769159\pi$
$479$			10.4744i			0.478588i	−0.970947	+	0.239294i	$0.923084\pi$
$480$	1.48002	−	4.80466i	0.0675532	−	0.219302i
$481$	−12.3042			−0.561024
$482$	12.0024			0.546692
$483$	36.5822	+	11.2687i	1.66455	+	0.512743i
$484$	−9.16150			−0.416432
$485$	−23.6896			−1.07569
$486$	−1.19484	−	15.5426i	−0.0541989	−	0.705027i
$487$	8.93084			0.404695			0.202348	−	0.979314i	$-0.435143\pi$
$487$	8.93084			0.404695			0.202348	+	0.979314i	$0.435143\pi$
$488$		−	10.6746i		−	0.483216i
$489$	3.07434	+	0.947014i	0.139027	+	0.0428254i
$490$			7.02346i			0.317288i
$491$			17.9966i			0.812175i	0.913834	+	0.406088i	$0.133107\pi$
$491$			17.9966i			0.812175i	−0.913834	+	0.406088i	$0.866893\pi$
$492$	−4.12710	+	13.3980i	−0.186064	+	0.604030i
$493$	1.37282			0.0618285
$494$		−	31.2453i		−	1.40579i
$495$	6.64361	−	9.76051i	0.298608	−	0.438702i
$496$			6.44875i			0.289557i
$497$			33.8853i			1.51996i
$498$	24.2507	+	7.47014i	1.08670	+	0.334745i
$499$	22.6464			1.01379			0.506897	−	0.862007i	$-0.330792\pi$
$499$	22.6464			1.01379			0.506897	+	0.862007i	$0.330792\pi$
$500$			4.57139i			0.204439i
$501$	−3.71391	+	12.0567i	−0.165925	+	0.538652i
$502$			2.86482i			0.127863i
$503$	24.9528			1.11259			0.556294	−	0.830985i	$-0.312223\pi$
$503$	24.9528			1.11259			0.556294	+	0.830985i	$0.312223\pi$
$504$	−7.61156	−	5.18089i	−0.339046	−	0.230775i
$505$			29.4947i			1.31250i
$506$	−9.76351			−0.434041
$507$	61.0099	+	18.7933i	2.70954	+	0.834642i
$508$	8.29304			0.367944
$509$	−8.75035			−0.387852			−0.193926	−	0.981016i	$-0.562122\pi$
$509$	−8.75035			−0.387852			−0.193926	+	0.981016i	$0.562122\pi$
$510$	2.73031	+	0.841039i	0.120900	+	0.0372418i
$511$			18.2935i			0.809258i
$512$	1.00000			0.0441942
$513$	14.3568	+	17.9603i	0.633870	+	0.792968i
$514$		−	11.8361i		−	0.522070i
$515$	−48.2848			−2.12768
$516$	0.392881	−	1.27543i	0.0172956	−	0.0561477i
$517$	−6.08651			−0.267685
$518$		−	5.34821i		−	0.234987i
$519$	−36.1700	−	11.1417i	−1.58769	−	0.489068i
$520$	−20.4952			−0.898772
$521$			6.33855i			0.277697i	0.990314	+	0.138848i	$0.0443401\pi$
$521$			6.33855i			0.277697i	−0.990314	+	0.138848i	$0.955660\pi$
$522$	4.07801	−	5.99125i	0.178490	−	0.262230i
$523$	2.35554			0.103001			0.0515003	−	0.998673i	$-0.483600\pi$
$523$	2.35554			0.103001			0.0515003	+	0.998673i	$0.483600\pi$
$524$	10.0063			0.437127
$525$	−17.4006	−	5.36004i	−0.759424	−	0.233931i
$526$			15.9639i			0.696057i
$527$	−3.66459			−0.159632
$528$	2.24444	+	0.691371i	0.0976766	+	0.0300881i
$529$	28.8500			1.25435
$530$	2.99858			0.130250
$531$	−4.25736	+	22.6467i	−0.184754	+	0.982785i
$532$	13.5812			0.588821
$533$	57.1518			2.47552
$534$	−19.0647	−	5.87266i	−0.825012	−	0.254135i
$535$	−56.7099			−2.45178
$536$			1.09256i			0.0471915i
$537$	−29.6936	−	9.14676i	−1.28137	−	0.394712i
$538$	−19.1392			−0.825152
$539$	−3.28092			−0.141319
$540$	11.7810	−	9.41729i	0.506973	−	0.405256i
$541$		−	38.4666i		−	1.65381i	−0.562343	−	0.826904i	$-0.690100\pi$
$541$		−	38.4666i		−	1.65381i	0.562343	−	0.826904i	$-0.309900\pi$
$542$	16.9434			0.727782
$543$	−2.69843	−	0.831217i	−0.115801	−	0.0356709i
$544$			0.568263i			0.0243641i
$545$	−4.12918			−0.176875
$546$	−11.0500	+	35.8723i	−0.472898	+	1.53519i
$547$	13.2301			0.565679			0.282840	−	0.959167i	$-0.408724\pi$
$547$	13.2301			0.565679			0.282840	+	0.959167i	$0.408724\pi$
$548$			12.8067i			0.547074i
$549$	18.0193	−	26.4732i	0.769043	−	1.12985i
$550$	4.64409			0.198025
$551$			10.6901i			0.455414i
$552$	−11.9193	−	3.67159i	−0.507319	−	0.156273i
$553$	−26.4574			−1.12508
$554$	17.8471			0.758252
$555$	8.37245	+	2.57903i	0.355391	+	0.109474i
$556$	8.09377			0.343252
$557$		−	26.6677i		−	1.12995i	−0.825109	−	0.564974i	$-0.808886\pi$
$557$		−	26.6677i		−	1.12995i	0.825109	−	0.564974i	$-0.191114\pi$
$558$	−10.8858	+	15.9930i	−0.460833	+	0.677038i
$559$	−5.44058			−0.230112
$560$		−	8.90852i		−	0.376454i
$561$	−0.392881	+	1.27543i	−0.0165874	+	0.0538487i
$562$		−	29.1267i		−	1.22863i
$563$	−22.5381			−0.949869			−0.474935	−	0.880021i	$-0.657528\pi$
$563$	−22.5381			−0.949869			−0.474935	+	0.880021i	$0.657528\pi$
$564$	−7.43042	−	2.28885i	−0.312877	−	0.0963779i
$565$			48.2931i			2.03170i
$566$			6.45672i			0.271396i
$567$	−10.1312	−	25.6974i	−0.425469	−	1.07919i
$568$		−	11.0406i		−	0.463253i
$569$	9.22568			0.386761			0.193380	−	0.981124i	$-0.438055\pi$
$569$	9.22568			0.386761			0.193380	+	0.981124i	$0.438055\pi$
$570$	−6.54917	+	21.2609i	−0.274315	+	0.890523i
$571$			34.5742i			1.44689i	0.690385	+	0.723443i	$0.257441\pi$
$571$			34.5742i			1.44689i	−0.690385	+	0.723443i	$0.742559\pi$
$572$		−	9.57406i		−	0.400311i
$573$	8.19093	+	2.52312i	0.342181	+	0.105405i
$574$			24.8419i			1.03688i
$575$	−24.6629			−1.02851
$576$	2.48002	+	1.68805i	0.103334	+	0.0703355i
$577$	16.2878			0.678070			0.339035	−	0.940774i	$-0.389899\pi$
$577$	16.2878			0.678070			0.339035	+	0.940774i	$0.389899\pi$
$578$	16.6771			0.693675
$579$	12.5108	+	3.85379i	0.519930	+	0.160158i
$580$	7.01212			0.291163
$581$	44.9643			1.86543
$582$	4.16150	−	13.5097i	0.172500	−	0.559996i
$583$			1.40075i			0.0580131i
$584$		−	5.96044i		−	0.246645i
$585$	−50.8283	−	34.5969i	−2.10149	−	1.43041i
$586$		−	28.9847i		−	1.19735i
$587$	23.7823			0.981600			0.490800	−	0.871272i	$-0.336705\pi$
$587$	23.7823			0.981600			0.490800	+	0.871272i	$0.336705\pi$
$588$	−4.00535	−	1.23380i	−0.165178	−	0.0508810i
$589$		−	28.5361i		−	1.17581i
$590$	−20.4314	+	8.92405i	−0.841146	+	0.367397i
$591$	3.33301	−	10.8201i	0.137102	−	0.445081i
$592$			1.74257i			0.0716191i
$593$		−	4.32008i		−	0.177404i	−0.996058	−	0.0887021i	$-0.971728\pi$
$593$		−	4.32008i		−	0.177404i	0.996058	−	0.0887021i	$-0.0282719\pi$
$594$	4.39917	+	5.50334i	0.180500	+	0.225805i
$595$	5.06238			0.207538
$596$	−12.4139			−0.508492
$597$	28.1304	+	8.66522i	1.15130	+	0.354644i
$598$			50.8439i			2.07916i
$599$			7.74067i			0.316275i	0.987417	+	0.158138i	$0.0505489\pi$
$599$			7.74067i			0.316275i	−0.987417	+	0.158138i	$0.949451\pi$
$600$	5.66950	+	1.74642i	0.231457	+	0.0712973i
$601$			12.8711i			0.525023i	0.964929	+	0.262512i	$0.0845508\pi$
$601$			12.8711i			0.525023i	−0.964929	+	0.262512i	$0.915449\pi$
$602$		−	2.36483i		−	0.0963832i
$603$	−1.84430	+	2.70957i	−0.0751057	+	0.110342i
$604$		−	6.74099i		−	0.274287i
$605$		−	26.5922i		−	1.08112i
$606$	−16.8203	−	5.18129i	−0.683278	−	0.210475i
$607$	−28.6668			−1.16355			−0.581775	−	0.813350i	$-0.697641\pi$
$607$	−28.6668			−1.16355			−0.581775	+	0.813350i	$0.697641\pi$
$608$	−4.42507			−0.179460
$609$	3.78061	−	12.2732i	0.153198	−	0.497335i
$610$	30.9840			1.25451
$611$			31.6958i			1.28228i
$612$	−0.959258	+	1.40930i	−0.0387757	+	0.0569677i
$613$			16.5246i			0.667421i	0.942676	+	0.333710i	$0.108301\pi$
$613$			16.5246i			0.667421i	−0.942676	+	0.333710i	$0.891699\pi$
$614$	5.63646			0.227469
$615$	−38.8891	−	11.9793i	−1.56816	−	0.483053i
$616$	4.16150			0.167672
$617$			10.8626i			0.437310i	0.975802	+	0.218655i	$0.0701670\pi$
$617$			10.8626i			0.437310i	−0.975802	+	0.218655i	$0.929833\pi$
$618$	8.48210	−	27.5359i	0.341200	−	1.10766i
$619$	25.8336			1.03834			0.519170	−	0.854671i	$-0.326241\pi$
$619$	25.8336			1.03834			0.519170	+	0.854671i	$0.326241\pi$
$620$	−18.7181			−0.751737
$621$	−23.3622	−	29.2260i	−0.937493	−	1.17280i
$622$		−	11.9919i		−	0.480833i
$623$	−35.3487			−1.41622
$624$	3.60035	−	11.6880i	0.144129	−	0.467895i
$625$	−30.3943			−1.21577
$626$		−	8.31980i		−	0.332526i
$627$	−9.93178	−	3.05936i	−0.396637	−	0.122179i
$628$			4.18807i			0.167122i
$629$	−0.990237			−0.0394833
$630$	15.0380	−	22.0933i	0.599130	−	0.880217i
$631$	21.7636			0.866395			0.433197	−	0.901299i	$-0.357385\pi$
$631$	21.7636			0.866395			0.433197	+	0.901299i	$0.357385\pi$
$632$	8.62041			0.342902
$633$	−14.2372	+	46.2190i	−0.565877	+	1.83704i
$634$			26.2936i			1.04425i
$635$			24.0714i			0.955243i
$636$	−0.526755	+	1.71003i	−0.0208872	+	0.0678073i
$637$			17.0856i			0.676955i
$638$			3.27562i			0.129683i
$639$	18.6371	−	27.3809i	0.737273	−	1.08317i
$640$			2.90260i			0.114735i
$641$		−	20.9447i		−	0.827265i	−0.910444	−	0.413633i	$-0.864260\pi$
$641$		−	20.9447i		−	0.827265i	0.910444	−	0.413633i	$-0.135740\pi$
$642$	9.96212	−	32.3406i	0.393173	−	1.27638i
$643$	2.51696			0.0992592			0.0496296	−	0.998768i	$-0.484196\pi$
$643$	2.51696			0.0992592			0.0496296	+	0.998768i	$0.484196\pi$
$644$	−22.1001			−0.870864
$645$	3.70206	+	1.14037i	0.145768	+	0.0449022i
$646$		−	2.51460i		−	0.0989357i
$647$			2.74431i			0.107890i	0.998544	+	0.0539450i	$0.0171796\pi$
$647$			2.74431i			0.107890i	−0.998544	+	0.0539450i	$0.982820\pi$
$648$	3.30096	+	8.37279i	0.129674	+	0.328914i
$649$	−4.16876	−	9.54425i	−0.163638	−	0.374645i
$650$		−	24.1843i		−	0.948587i
$651$	−10.0919	+	32.7620i	−0.395534	+	1.28404i
$652$	−1.85728			−0.0727365
$653$		−	16.8300i		−	0.658609i	−0.944224	−	0.329304i	$-0.893186\pi$
$653$		−	16.8300i		−	0.658609i	0.944224	−	0.329304i	$-0.106814\pi$
$654$	0.725366	−	2.35480i	0.0283640	−	0.0920798i
$655$			29.0442i			1.13485i
$656$		−	8.09404i		−	0.316019i
$657$	10.0615	−	14.7820i	0.392538	−	0.576700i
$658$	−13.7770			−0.537085
$659$	28.5754			1.11314			0.556570	−	0.830801i	$-0.312117\pi$
$659$	28.5754			1.11314			0.556570	+	0.830801i	$0.312117\pi$
$660$	−2.00677	+	6.51469i	−0.0781135	+	0.253584i
$661$	−5.84243			−0.227244			−0.113622	−	0.993524i	$-0.536245\pi$
$661$	−5.84243			−0.227244			−0.113622	+	0.993524i	$0.536245\pi$
$662$	−20.2592			−0.787396
$663$	6.64187	+	2.04595i	0.257949	+	0.0794579i
$664$	−14.6504			−0.568545
$665$			39.4208i			1.52867i
$666$	−2.94154	+	4.32160i	−0.113983	+	0.167458i
$667$		−	17.3955i		−	0.673557i
$668$		−	7.28369i		−	0.281814i
$669$	35.8010	+	11.0280i	1.38415	+	0.426369i
$670$	−3.17127			−0.122517
$671$			14.4738i			0.558755i
$672$	5.08036	+	1.56494i	0.195979	+	0.0603690i
$673$		−	8.90428i		−	0.343235i	−0.985164	−	0.171617i	$-0.945101\pi$
$673$		−	8.90428i		−	0.343235i	0.985164	−	0.171617i	$-0.0548993\pi$
$674$		−	33.0786i		−	1.27414i
$675$	11.1124	+	13.9016i	0.427717	+	0.535072i
$676$	−36.8574			−1.41759
$677$		−	8.80973i		−	0.338585i	−0.985566	−	0.169293i	$-0.945852\pi$
$677$		−	8.80973i		−	0.338585i	0.985566	−	0.169293i	$-0.0541483\pi$
$678$	−27.5406	−	8.48356i	−1.05769	−	0.325809i
$679$		−	25.0489i		−	0.961290i
$680$	−1.64944			−0.0632531
$681$	0.788552	+	0.242904i	0.0302174	+	0.00930809i
$682$		−	8.74393i		−	0.334822i
$683$	−24.8965			−0.952637			−0.476318	−	0.879273i	$-0.658029\pi$
$683$	−24.8965			−0.952637			−0.476318	+	0.879273i	$0.658029\pi$
$684$	−10.9742	−	7.46974i	−0.419611	−	0.285613i
$685$	−37.1726			−1.42029
$686$	14.0576			0.536722
$687$	9.21153	−	29.9039i	0.351442	−	1.14091i
$688$			0.770515i			0.0293756i
$689$	7.29446			0.277897
$690$	10.6571	−	34.5969i	0.405711	−	1.31708i
$691$		−	23.9319i		−	0.910413i	−0.890386	−	0.455206i	$-0.849565\pi$
$691$		−	23.9319i		−	0.910413i	0.890386	−	0.455206i	$-0.150435\pi$
$692$	21.8511			0.830653
$693$	10.3206	+	7.02483i	0.392047	+	0.266851i
$694$	−20.5577			−0.780358
$695$			23.4929i			0.891138i
$696$	−1.23181	+	3.99888i	−0.0466915	+	0.151577i
$697$	4.59955			0.174220
$698$			26.3694i			0.998098i
$699$	12.9648	+	3.99364i	0.490373	+	0.151053i
$700$	10.5121			0.397319
$701$	25.7011			0.970717			0.485358	−	0.874315i	$-0.338689\pi$
$701$	25.7011			0.970717			0.485358	+	0.874315i	$0.338689\pi$
$702$	28.6589	−	22.9089i	1.08166	−	0.864640i
$703$		−	7.71098i		−	0.290825i
$704$	−1.35591			−0.0511028
$705$	6.64361	−	21.5675i	0.250213	−	0.812279i
$706$	16.1784			0.608884
$707$	−31.1872			−1.17292
$708$	−1.50008	−	13.2193i	−0.0563765	−	0.496812i
$709$	−37.5287			−1.40942			−0.704710	−	0.709496i	$-0.748923\pi$
$709$	−37.5287			−1.40942			−0.704710	+	0.709496i	$0.748923\pi$
$710$	32.0464			1.20268
$711$	21.3788	+	14.5517i	0.801766	+	0.545732i
$712$	11.5174			0.431633
$713$			46.4355i			1.73902i
$714$	−0.889300	+	2.88698i	−0.0332812	+	0.108043i
$715$	27.7896			1.03927
$716$	17.9386			0.670395
$717$	−6.69503	+	21.7344i	−0.250030	+	0.811688i
$718$		−	19.3351i		−	0.721580i
$719$	35.0768			1.30815			0.654073	−	0.756432i	$-0.273059\pi$
$719$	35.0768			1.30815			0.654073	+	0.756432i	$0.273059\pi$
$720$	−4.89973	+	7.19849i	−0.182602	+	0.268272i
$721$		−	51.0555i		−	1.90141i
$722$	0.581221			0.0216308
$723$	−19.8675	−	6.11993i	−0.738879	−	0.227603i
$724$	1.63018			0.0605850
$725$			8.27431i			0.307300i
$726$	15.1650	+	4.67140i	0.562826	+	0.173372i
$727$	37.6281			1.39555			0.697775	−	0.716317i	$-0.254174\pi$
$727$	37.6281			1.39555			0.697775	+	0.716317i	$0.254174\pi$
$728$		−	21.6712i		−	0.803189i
$729$	−5.94727	+	26.3369i	−0.220269	+	0.975439i
$730$	17.3008			0.640330
$731$	−0.437855			−0.0161947
$732$	−5.44291	+	17.6696i	−0.201176	+	0.653088i
$733$	−18.3230			−0.676776			−0.338388	−	0.941007i	$-0.609882\pi$
$733$	−18.3230			−0.676776			−0.338388	+	0.941007i	$0.609882\pi$
$734$		−	7.18946i		−	0.265368i
$735$	3.58122	−	11.6259i	0.132095	−	0.428828i
$736$	7.20070			0.265421
$737$		−	1.48142i		−	0.0545687i
$738$	13.6632	−	20.0734i	0.502948	−	0.738910i
$739$			37.2587i			1.37058i	0.728270	+	0.685291i	$0.240325\pi$
$739$			37.2587i			1.37058i	−0.728270	+	0.685291i	$0.759675\pi$
$740$	−5.05797			−0.185935
$741$	−15.9318	+	51.7202i	−0.585269	+	1.89999i
$742$			3.17065i			0.116398i
$743$		−	21.2235i		−	0.778614i	−0.921108	−	0.389307i	$-0.872715\pi$
$743$		−	21.2235i		−	0.778614i	0.921108	−	0.389307i	$-0.127285\pi$
$744$	3.28818	−	10.6746i	0.120550	−	0.391350i
$745$		−	36.0325i		−	1.32013i
$746$	20.0865			0.735420
$747$	−36.3332	−	24.7306i	−1.32936	−	0.904845i
$748$		−	0.770515i		−	0.0281728i
$749$		−	59.9640i		−	2.19104i
$750$	2.33093	−	7.56702i	0.0851134	−	0.276308i
$751$			24.3301i			0.887817i	0.896072	+	0.443908i	$0.146408\pi$
$751$			24.3301i			0.887817i	−0.896072	+	0.443908i	$0.853592\pi$
$752$	4.48887			0.163692
$753$	1.46075	−	4.74212i	0.0532328	−	0.172813i
$754$	17.0580			0.621215
$755$	19.5664			0.712093
$756$	9.95768	+	12.4570i	0.362157	+	0.453057i
$757$	32.8729			1.19479			0.597393	−	0.801949i	$-0.296203\pi$
$757$	32.8729			1.19479			0.597393	+	0.801949i	$0.296203\pi$
$758$	2.68186			0.0974095
$759$	16.1615	+	4.97835i	0.586625	+	0.180703i
$760$		−	12.8442i		−	0.465908i
$761$		−	15.2935i		−	0.554390i	−0.960814	−	0.277195i	$-0.910595\pi$
$761$		−	15.2935i		−	0.554390i	0.960814	−	0.277195i	$-0.0894048\pi$
$762$	−13.7275	−	4.22857i	−0.497293	−	0.153185i
$763$		−	4.36613i		−	0.158064i
$764$	−4.94832			−0.179024
$765$	−4.09064	−	2.78434i	−0.147897	−	0.100668i
$766$		−	22.1048i		−	0.798680i
$767$	−49.7021	+	21.7090i	−1.79464	+	0.783867i
$768$	−1.65530	−	0.509894i	−0.0597304	−	0.0183992i
$769$			11.7785i			0.424745i	0.977189	+	0.212372i	$0.0681190\pi$
$769$			11.7785i			0.424745i	−0.977189	+	0.212372i	$0.931881\pi$
$770$			12.0792i			0.435303i
$771$	−6.03518	+	19.5923i	−0.217352	+	0.705600i
$772$	−7.55803			−0.272019
$773$	0.997271			0.0358694			0.0179347	−	0.999839i	$-0.494291\pi$
$773$	0.997271			0.0358694			0.0179347	+	0.999839i	$0.494291\pi$
$774$	−1.30067	+	1.91089i	−0.0467516	+	0.0686855i
$775$		−	22.0874i		−	0.793403i
$776$			8.16151i			0.292981i
$777$	−2.72702	+	8.85288i	−0.0978313	+	0.317595i
$778$		−	1.33259i		−	0.0477757i
$779$			35.8167i			1.28327i
$780$	33.9256	+	10.4504i	1.21473	+	0.374183i
$781$			14.9701i			0.535672i
$782$			4.09189i			0.146326i
$783$	−9.80522	+	7.83794i	−0.350410	+	0.280105i
$784$	2.41972			0.0864185
$785$	−12.1563			−0.433876
$786$	−16.5634	−	5.10215i	−0.590796	−	0.181988i
$787$	−16.0938			−0.573681			−0.286840	−	0.957978i	$-0.592605\pi$
$787$	−16.0938			−0.573681			−0.286840	+	0.957978i	$0.592605\pi$
$788$			6.53668i			0.232859i
$789$	8.13987	−	26.4249i	0.289787	−	0.940752i
$790$			25.0216i			0.890228i
$791$	−51.0643			−1.81564
$792$	−3.36268	−	2.28885i	−0.119488	−	0.0813307i
$793$	75.3730			2.67657
$794$		−	25.3810i		−	0.900739i
$795$	−4.96354	−	1.52896i	−0.176039	−	0.0542265i
$796$	−16.9942			−0.602342
$797$	−12.5629			−0.445001			−0.222500	−	0.974933i	$-0.571422\pi$
$797$	−12.5629			−0.445001			−0.222500	+	0.974933i	$0.571422\pi$
$798$	−22.4810	−	6.92498i	−0.795817	−	0.245142i
$799$			2.55086i			0.0902430i
$800$	−3.42507			−0.121094
$801$	28.5634	+	19.4420i	1.00924	+	0.686949i
$802$	−14.2292			−0.502452
$803$			8.08183i			0.285202i
$804$	0.557091	−	1.80851i	0.0196471	−	0.0637814i
$805$		−	64.1476i		−	2.26090i
$806$	−45.5344			−1.60388
$807$	31.6811	+	9.75899i	1.11523	+	0.343533i
$808$	10.1615			0.357480
$809$	3.23293			0.113664			0.0568319	−	0.998384i	$-0.481900\pi$
$809$	3.23293			0.113664			0.0568319	+	0.998384i	$0.481900\pi$
$810$	−24.3028	+	9.58136i	−0.853915	+	0.336655i
$811$		−	23.6153i		−	0.829247i	−0.909993	−	0.414623i	$-0.863913\pi$
$811$		−	23.6153i		−	0.829247i	0.909993	−	0.414623i	$-0.136087\pi$
$812$			7.41450i			0.260198i
$813$	−28.0464	−	8.63935i	−0.983630	−	0.302995i
$814$		−	2.36277i		−	0.0828150i
$815$		−	5.39092i		−	0.188836i
$816$	0.289754	−	0.940644i	0.0101434	−	0.0329291i
$817$		−	3.40958i		−	0.119286i
$818$			15.8746i			0.555041i
$819$	36.5822	−	53.7450i	1.27828	−	1.87800i
$820$	23.4937			0.820437
$821$	−12.6014			−0.439793			−0.219896	−	0.975523i	$-0.570572\pi$
$821$	−12.6014			−0.439793			−0.219896	+	0.975523i	$0.570572\pi$
$822$	6.53004	−	21.1988i	0.227761	−	0.739395i
$823$		−	14.1417i		−	0.492949i	−0.969149	−	0.246475i	$-0.920728\pi$
$823$		−	14.1417i		−	0.492949i	0.969149	−	0.246475i	$-0.0792722\pi$
$824$			16.6350i			0.579509i
$825$	−7.68735	−	2.36799i	−0.267639	−	0.0824429i
$826$	−9.43614	−	21.6038i	−0.328325	−	0.751691i
$827$			30.0311i			1.04429i	0.852858	+	0.522143i	$0.174867\pi$
$827$			30.0311i			1.04429i	−0.852858	+	0.522143i	$0.825133\pi$
$828$	17.8578	+	12.1551i	0.620603	+	0.422421i
$829$	−41.2477			−1.43259			−0.716296	−	0.697797i	$-0.754164\pi$
$829$	−41.2477			−1.43259			−0.716296	+	0.697797i	$0.754164\pi$
$830$		−	42.5241i		−	1.47603i
$831$	−29.5423	−	9.10015i	−1.02481	−	0.315681i
$832$			7.06097i			0.244795i
$833$			1.37504i			0.0476422i
$834$	−13.3976	−	4.12696i	−0.463921	−	0.142905i
$835$	21.1416			0.731636
$836$	6.00000			0.207514
$837$	26.1740	−	20.9225i	0.904706	−	0.723189i
$838$	−16.8244			−0.581188
$839$	−39.0484			−1.34810			−0.674050	−	0.738686i	$-0.735447\pi$
$839$	−39.0484			−1.34810			−0.674050	+	0.738686i	$0.735447\pi$
$840$	−4.54240	+	14.7462i	−0.156728	+	0.508794i
$841$	23.1639			0.798754
$842$			4.37616i			0.150812i
$843$	−14.8515	+	48.2133i	−0.511513	+	1.66055i
$844$		−	27.9219i		−	0.961110i
$845$		−	106.982i		−	3.68029i
$846$	11.1325	+	7.57745i	0.382742	+	0.260518i
$847$	28.1181			0.966149
$848$		−	1.03307i		−	0.0354757i
$849$	3.29224	−	10.6878i	0.112989	−	0.366804i
$850$		−	1.94634i		−	0.0667589i
$851$			12.5477i			0.430130i
$852$	−5.62954	+	18.2755i	−0.192865	+	0.626108i
$853$	41.7782			1.43046			0.715230	−	0.698890i	$-0.246322\pi$
$853$	41.7782			1.43046			0.715230	+	0.698890i	$0.246322\pi$
$854$			32.7620i			1.12109i
$855$	21.6817	−	31.8538i	0.741497	−	1.08938i
$856$			19.5376i			0.667782i
$857$	−39.5730			−1.35179			−0.675893	−	0.736999i	$-0.736242\pi$
$857$	−39.5730			−1.35179			−0.675893	+	0.736999i	$0.736242\pi$
$858$	−4.88175	+	15.8479i	−0.166660	+	0.541039i
$859$		−	25.8673i		−	0.882580i	−0.897365	−	0.441290i	$-0.854521\pi$
$859$		−	25.8673i		−	0.882580i	0.897365	−	0.441290i	$-0.145479\pi$
$860$	−2.23649			−0.0762638
$861$	12.6667	−	41.1207i	0.431681	−	1.40139i
$862$	−2.04895			−0.0697877
$863$	−18.9288			−0.644344			−0.322172	−	0.946681i	$-0.604413\pi$
$863$	−18.9288			−0.644344			−0.322172	+	0.946681i	$0.604413\pi$
$864$	−3.24444	−	4.05877i	−0.110378	−	0.138082i
$865$			63.4248i			2.15651i
$866$	−29.6427			−1.00730
$867$	−27.6055	−	8.50354i	−0.937532	−	0.288795i
$868$		−	19.7922i		−	0.671791i
$869$	−11.6885			−0.396506
$870$	−11.6071	−	3.57544i	−0.393519	−	0.121219i
$871$	−7.71455			−0.261398
$872$			1.42258i			0.0481747i
$873$	−13.7770	+	20.2407i	−0.466282	+	0.685043i
$874$	−31.8636			−1.07780
$875$		−	14.0303i		−	0.474311i
$876$	−3.03919	+	9.86630i	−0.102685	+	0.333351i
$877$	−37.8935			−1.27957			−0.639787	−	0.768552i	$-0.720977\pi$
$877$	−37.8935			−1.27957			−0.639787	+	0.768552i	$0.720977\pi$
$878$	−22.0490			−0.744119
$879$	−14.7791	+	47.9783i	−0.498488	+	1.61827i
$880$		−	3.93566i		−	0.132671i
$881$	51.8993			1.74853			0.874266	−	0.485448i	$-0.161343\pi$
$881$	51.8993			1.74853			0.874266	+	0.485448i	$0.161343\pi$
$882$	6.00094	+	4.08461i	0.202062	+	0.137536i
$883$	38.2326			1.28663			0.643316	−	0.765601i	$-0.277558\pi$
$883$	38.2326			1.28663			0.643316	+	0.765601i	$0.277558\pi$
$884$	−4.01249			−0.134955
$885$	38.3703	−	4.35413i	1.28980	−	0.146363i
$886$	8.23544			0.276675
$887$	39.7271			1.33391			0.666953	−	0.745100i	$-0.267598\pi$
$887$	39.7271			1.33391			0.666953	+	0.745100i	$0.267598\pi$
$888$	0.888525	−	2.88447i	0.0298169	−	0.0967964i
$889$	−25.4526			−0.853654
$890$			33.4304i			1.12059i
$891$	−4.47581	−	11.3528i	−0.149945	−	0.380332i
$892$	−21.6281			−0.724163
$893$	−19.8636			−0.664709
$894$	20.5487	+	6.32976i	0.687250	+	0.211699i
$895$			52.0684i			1.74045i
$896$	−3.06916			−0.102533
$897$	25.9250	−	84.1618i	0.865611	−	2.81008i
$898$		−	1.44717i		−	0.0482926i
$899$	15.5789			0.519587
$900$	−8.49422	−	5.78169i	−0.283141	−	0.192723i
$901$	0.587054			0.0195576
$902$			10.9748i			0.365421i
$903$	−1.20581	+	3.91449i	−0.0401269	+	0.130266i
$904$	16.6379			0.553368
$905$			4.73174i			0.157288i
$906$	−3.43719	+	11.1583i	−0.114193	+	0.370711i
$907$	−26.0657			−0.865497			−0.432748	−	0.901515i	$-0.642456\pi$
$907$	−26.0657			−0.865497			−0.432748	+	0.901515i	$0.642456\pi$
$908$	−0.476381			−0.0158093
$909$	25.2007	+	17.1531i	0.835854	+	0.568934i
$910$	62.9028			2.08521
$911$			55.8967i			1.85194i	0.377595	+	0.925971i	$0.376751\pi$
$911$			55.8967i			1.85194i	−0.377595	+	0.925971i	$0.623249\pi$
$912$	7.32480	+	2.25631i	0.242548	+	0.0747141i
$913$	19.8646			0.657423
$914$			22.1516i			0.732709i
$915$	−51.2878	−	15.7986i	−1.69552	−	0.522285i
$916$			18.0656i			0.596904i
$917$	−30.7109			−1.01416
$918$	2.30645	−	1.84369i	0.0761242	−	0.0608510i
$919$			21.9514i			0.724109i	0.932157	+	0.362055i	$0.117925\pi$
$919$			21.9514i			0.724109i	−0.932157	+	0.362055i	$0.882075\pi$
$920$			20.9007i			0.689076i
$921$	−9.33002	−	2.87400i	−0.307435	−	0.0947015i
$922$		−	17.2878i		−	0.569344i
$923$	77.9574			2.56600
$924$	−6.88852	−	2.12193i	−0.226616	−	0.0698062i
$925$		−	5.96841i		−	0.196240i
$926$			14.3744i			0.472370i
$927$	−28.0808	+	41.2552i	−0.922294	+	1.35500i
$928$		−	2.41581i		−	0.0793028i
$929$	−41.6039			−1.36498			−0.682490	−	0.730895i	$-0.739103\pi$
$929$	−41.6039			−1.36498			−0.682490	+	0.730895i	$0.739103\pi$
$930$	30.9840	+	9.54425i	1.01601	+	0.312968i
$931$	−10.7074			−0.350921
$932$	−7.83229			−0.256555
$933$	−6.11461	+	19.8502i	−0.200183	+	0.649866i
$934$	−23.6209			−0.772898
$935$	2.23649			0.0731411
$936$	−11.9193	+	17.5113i	−0.389594	+	0.572376i
$937$		−	27.8177i		−	0.908765i	−0.890807	−	0.454382i	$-0.849860\pi$
$937$		−	27.8177i		−	0.908765i	0.890807	−	0.454382i	$-0.150140\pi$
$938$		−	3.35324i		−	0.109487i
$939$	−4.24221	+	13.7717i	−0.138439	+	0.449424i
$940$			13.0294i			0.424972i
$941$	55.9681			1.82451			0.912253	−	0.409626i	$-0.134341\pi$
$941$	55.9681			1.82451			0.912253	+	0.409626i	$0.134341\pi$
$942$	2.13547	−	6.93249i	0.0695774	−	0.225873i
$943$		−	58.2827i		−	1.89795i
$944$	3.07451	+	7.03899i	0.100067	+	0.229100i
$945$	−36.1577	+	28.9031i	−1.17621	+	0.940219i
$946$		−	1.04475i		−	0.0339677i
$947$			7.20150i			0.234017i	0.993131	+	0.117009i	$0.0373305\pi$
$947$			7.20150i			0.234017i	−0.993131	+	0.117009i	$0.962669\pi$
$948$	−14.2693	−	4.39550i	−0.463447	−	0.142759i
$949$	42.0865			1.36619
$950$	15.1562			0.491731
$951$	13.4069	−	43.5237i	0.434750	−	1.41135i
$952$		−	1.74409i		−	0.0565262i
$953$		−	10.7126i		−	0.347017i	−0.984832	−	0.173508i	$-0.944490\pi$
$953$		−	10.7126i		−	0.347017i	0.984832	−	0.173508i	$-0.0555103\pi$
$954$	1.74387	−	2.56202i	0.0564599	−	0.0829486i
$955$		−	14.3630i		−	0.464775i
$956$		−	13.1302i		−	0.424662i
$957$	1.67022	−	5.42213i	0.0539906	−	0.175273i
$958$			10.4744i			0.338413i
$959$		−	39.3057i		−	1.26925i
$960$	1.48002	−	4.80466i	0.0477673	−	0.155070i
$961$	−10.5863			−0.341495
$962$	−12.3042			−0.396704
$963$	−32.9805	+	48.4536i	−1.06278	+	1.56140i
$964$	12.0024			0.386570
$965$		−	21.9379i		−	0.706206i
$966$	36.5822	+	11.2687i	1.17701	+	0.362564i
$967$			2.93722i			0.0944545i	0.998884	+	0.0472273i	$0.0150385\pi$
$967$			2.93722i			0.0944545i	−0.998884	+	0.0472273i	$0.984961\pi$
$968$	−9.16150			−0.294462
$969$	−1.28218	+	4.16241i	−0.0411896	+	0.133716i
$970$	−23.6896			−0.760626
$971$		−	13.6005i		−	0.436462i	−0.975897	−	0.218231i	$-0.929971\pi$
$971$		−	13.6005i		−	0.436462i	0.975897	−	0.218231i	$-0.0700286\pi$
$972$	−1.19484	−	15.5426i	−0.0383244	−	0.498529i
$973$	−24.8410			−0.796367
$974$	8.93084			0.286163
$975$	−12.3314	+	40.0322i	−0.394922	+	1.28206i
$976$		−	10.6746i		−	0.341685i
$977$	17.9615			0.574638			0.287319	−	0.957835i	$-0.407236\pi$
$977$	17.9615			0.574638			0.287319	+	0.957835i	$0.407236\pi$
$978$	3.07434	+	0.947014i	0.0983067	+	0.0302822i
$979$	−15.6166			−0.499109
$980$			7.02346i			0.224356i
$981$	−2.40139	+	3.52803i	−0.0766705	+	0.112641i
$982$			17.9966i			0.574295i
$983$	10.2409			0.326635			0.163318	−	0.986574i	$-0.447780\pi$
$983$	10.2409			0.326635			0.163318	+	0.986574i	$0.447780\pi$
$984$	−4.12710	+	13.3980i	−0.131567	+	0.427114i
$985$	−18.9733			−0.604541
$986$	1.37282			0.0437194
$987$	22.8051	+	7.02483i	0.725895	+	0.223603i
$988$		−	31.2453i		−	0.994045i
$989$			5.54824i			0.176424i
$990$	6.64361	−	9.76051i	0.211148	−	0.310209i
$991$		−	19.6544i		−	0.624343i	−0.950026	−	0.312172i	$-0.898944\pi$
$991$		−	19.6544i		−	0.624343i	0.950026	−	0.312172i	$-0.101056\pi$
$992$			6.44875i			0.204748i
$993$	33.5350	+	10.3300i	1.06420	+	0.327814i
$994$			33.8853i			1.07478i
$995$		−	49.3272i		−	1.56378i
$996$	24.2507	+	7.47014i	0.768414	+	0.236700i
$997$	−34.3733			−1.08861			−0.544307	−	0.838886i	$-0.683207\pi$
$997$	−34.3733			−1.08861			−0.544307	+	0.838886i	$0.683207\pi$
$998$	22.6464			0.716861
$999$	7.07269	−	5.65365i	0.223770	−	0.178874i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.2.c.b.353.1	yes	10
3.2	odd	2		354.2.c.a.353.2	yes	10
59.58	odd	2		354.2.c.a.353.1	✓	10
177.176	even	2	inner	354.2.c.b.353.2	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.2.c.a.353.1	✓	10	59.58	odd	2
354.2.c.a.353.2	yes	10	3.2	odd	2
354.2.c.b.353.1	yes	10	1.1	even	1	trivial
354.2.c.b.353.2	yes	10	177.176	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	354.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(-1.65530 - 0.509894i) q^{3} +1.00000 q^{4} +2.90260i q^{5} +(-1.65530 - 0.509894i) q^{6} -3.06916 q^{7} +1.00000 q^{8} +(2.48002 + 1.68805i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(-1.65530 - 0.509894i) q^{3} +1.00000 q^{4} +2.90260i q^{5} +(-1.65530 - 0.509894i) q^{6} -3.06916 q^{7} +1.00000 q^{8} +(2.48002 + 1.68805i) q^{9} +2.90260i q^{10} -1.35591 q^{11} +(-1.65530 - 0.509894i) q^{12} +7.06097i q^{13} -3.06916 q^{14} +(1.48002 - 4.80466i) q^{15} +1.00000 q^{16} +0.568263i q^{17} +(2.48002 + 1.68805i) q^{18} -4.42507 q^{19} +2.90260i q^{20} +(5.08036 + 1.56494i) q^{21} -1.35591 q^{22} +7.20070 q^{23} +(-1.65530 - 0.509894i) q^{24} -3.42507 q^{25} +7.06097i q^{26} +(-3.24444 - 4.05877i) q^{27} -3.06916 q^{28} -2.41581i q^{29} +(1.48002 - 4.80466i) q^{30} +6.44875i q^{31} +1.00000 q^{32} +(2.24444 + 0.691371i) q^{33} +0.568263i q^{34} -8.90852i q^{35} +(2.48002 + 1.68805i) q^{36} +1.74257i q^{37} -4.42507 q^{38} +(3.60035 - 11.6880i) q^{39} +2.90260i q^{40} -8.09404i q^{41} +(5.08036 + 1.56494i) q^{42} +0.770515i q^{43} -1.35591 q^{44} +(-4.89973 + 7.19849i) q^{45} +7.20070 q^{46} +4.48887 q^{47} +(-1.65530 - 0.509894i) q^{48} +2.41972 q^{49} -3.42507 q^{50} +(0.289754 - 0.940644i) q^{51} +7.06097i q^{52} -1.03307i q^{53} +(-3.24444 - 4.05877i) q^{54} -3.93566i q^{55} -3.06916 q^{56} +(7.32480 + 2.25631i) q^{57} -2.41581i q^{58} +(3.07451 + 7.03899i) q^{59} +(1.48002 - 4.80466i) q^{60} -10.6746i q^{61} +6.44875i q^{62} +(-7.61156 - 5.18089i) q^{63} +1.00000 q^{64} -20.4952 q^{65} +(2.24444 + 0.691371i) q^{66} +1.09256i q^{67} +0.568263i q^{68} +(-11.9193 - 3.67159i) q^{69} -8.90852i q^{70} -11.0406i q^{71} +(2.48002 + 1.68805i) q^{72} -5.96044i q^{73} +1.74257i q^{74} +(5.66950 + 1.74642i) q^{75} -4.42507 q^{76} +4.16150 q^{77} +(3.60035 - 11.6880i) q^{78} +8.62041 q^{79} +2.90260i q^{80} +(3.30096 + 8.37279i) q^{81} -8.09404i q^{82} -14.6504 q^{83} +(5.08036 + 1.56494i) q^{84} -1.64944 q^{85} +0.770515i q^{86} +(-1.23181 + 3.99888i) q^{87} -1.35591 q^{88} +11.5174 q^{89} +(-4.89973 + 7.19849i) q^{90} -21.6712i q^{91} +7.20070 q^{92} +(3.28818 - 10.6746i) q^{93} +4.48887 q^{94} -12.8442i q^{95} +(-1.65530 - 0.509894i) q^{96} +8.16151i q^{97} +2.41972 q^{98} +(-3.36268 - 2.28885i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 10 q^{2} - q^{3} + 10 q^{4} - q^{6} - 2 q^{7} + 10 q^{8} + 3 q^{9}+O(q^{10}) \) 10 * q + 10 * q^2 - q^3 + 10 * q^4 - q^6 - 2 * q^7 + 10 * q^8 + 3 * q^9	\( 10 q + 10 q^{2} - q^{3} + 10 q^{4} - q^{6} - 2 q^{7} + 10 q^{8} + 3 q^{9} - 4 q^{11} - q^{12} - 2 q^{14} - 7 q^{15} + 10 q^{16} + 3 q^{18} - 6 q^{19} - 3 q^{21} - 4 q^{22} + 8 q^{23} - q^{24} + 4 q^{25} - 10 q^{27} - 2 q^{28} - 7 q^{30} + 10 q^{32} + 3 q^{36} - 6 q^{38} + 4 q^{39} - 3 q^{42} - 4 q^{44} - 11 q^{45} + 8 q^{46} - q^{48} + 8 q^{49} + 4 q^{50} + 2 q^{51} - 10 q^{54} - 2 q^{56} - 3 q^{57} - 20 q^{59} - 7 q^{60} - 19 q^{63} + 10 q^{64} - 16 q^{65} - 14 q^{69} + 3 q^{72} - 4 q^{75} - 6 q^{76} - 48 q^{77} + 4 q^{78} + 6 q^{79} + 7 q^{81} - 12 q^{83} - 3 q^{84} - 4 q^{85} - 15 q^{87} - 4 q^{88} + 16 q^{89} - 11 q^{90} + 8 q^{92} + 52 q^{93} - q^{96} + 8 q^{98} - 2 q^{99}+O(q^{100}) \) 10 * q + 10 * q^2 - q^3 + 10 * q^4 - q^6 - 2 * q^7 + 10 * q^8 + 3 * q^9 - 4 * q^11 - q^12 - 2 * q^14 - 7 * q^15 + 10 * q^16 + 3 * q^18 - 6 * q^19 - 3 * q^21 - 4 * q^22 + 8 * q^23 - q^24 + 4 * q^25 - 10 * q^27 - 2 * q^28 - 7 * q^30 + 10 * q^32 + 3 * q^36 - 6 * q^38 + 4 * q^39 - 3 * q^42 - 4 * q^44 - 11 * q^45 + 8 * q^46 - q^48 + 8 * q^49 + 4 * q^50 + 2 * q^51 - 10 * q^54 - 2 * q^56 - 3 * q^57 - 20 * q^59 - 7 * q^60 - 19 * q^63 + 10 * q^64 - 16 * q^65 - 14 * q^69 + 3 * q^72 - 4 * q^75 - 6 * q^76 - 48 * q^77 + 4 * q^78 + 6 * q^79 + 7 * q^81 - 12 * q^83 - 3 * q^84 - 4 * q^85 - 15 * q^87 - 4 * q^88 + 16 * q^89 - 11 * q^90 + 8 * q^92 + 52 * q^93 - q^96 + 8 * q^98 - 2 * q^99

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